Structure formation mechanisms in consolidating pigment coatings—Simulation and visualisation

Structure formation mechanisms in consolidating pigment coatings—Simulation and visualisation

Chemical Engineering and Processing 50 (2011) 574–582 Contents lists available at ScienceDirect Chemical Engineering and Processing: Process Intensi...

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Chemical Engineering and Processing 50 (2011) 574–582

Contents lists available at ScienceDirect

Chemical Engineering and Processing: Process Intensification journal homepage:

Structure formation mechanisms in consolidating pigment coatings—Simulation and visualisation Anders Sand a,∗ , Jani Kniivilä a , Martti Toivakka a,1 , Tuomo Hjelt b,2 a b

Laboratory of Paper Coating and Converting, and Centre for Functional Materials, Åbo Akademi University, Porthaninkatu 3, 20500 Turku, Finland VTT, Tekniikantie 2, 02150 Espoo, Finland

a r t i c l e

i n f o

Article history: Received 25 March 2010 Received in revised form 5 August 2010 Accepted 6 September 2010 Available online 21 September 2010 Keywords: Pigment coating Clustering Colloidal interactions Consolidation Drying Dynamics

a b s t r a c t Microstructure development in consolidating pigment coating layers was studied in terms of particle flocculation and clustering mechanisms utilising a 3D particle dynamics model. The model includes hydrodynamic forces, colloidal interactions as well as the Brownian motion. The influence of colloidal interactions and drying strategy on the coating layer thickness development and internal solid concentration gradients, was investigated. A low particle surface potential resulted in the formation of porous particle networks, which impeded the shrinkage of the coating layer. At higher surface potentials particles arranged into denser structures, whereby the solids concentration profile could be controlled by the drying. Low electrostatic double layer thicknesses allowed sharp concentration gradients to form as result of the applied drying strategy. At high double layer thicknesses, the structure formation was similar regardless of drying strategy. This work elucidates the combined effect of drying conditions and colloidal suspension properties on coating microstructure development. Furthermore, the results aid in the understanding of how coating suspension additives may influence the structure development of the coating layer. © 2010 Elsevier B.V. All rights reserved.

1. Introduction There are several industrial processes which are based on the application of a particle suspension onto a porous base substrate in order to improve its surface properties. Paper coating or other surface treatments such as painting or printing are but a few examples. The objective in these processes is usually to obtain a surface layer with desired physical and functional attributes, which could include e.g. improved optical, mechanical or barrier properties [1,2]. Once the coating layer has been applied, its solids content gradually increases through loss of liquid phase into the base substrate through capillary absorption, as well as evaporation through drying. The consolidation of a pigment coating has traditionally been divided into three phases, separated by experimentally observable changes in the optical properties of the coating [3]. The first critical concentration, FCC, is reached when solid particles start to penetrate the surface of the coating, resulting in a sharp drop in surface

∗ Corresponding author. Tel.: +358 2 215 4894; fax: +358 2 215 3226. E-mail addresses: [email protected]fi, [email protected]fi (A. Sand), [email protected]fi (J. Kniivilä), [email protected]fi (M. Toivakka), [email protected]fi (T. Hjelt). 1 Tel.: +358 2 215 4852; fax: +358 2 215 3226. 2 Tel.: +358 20 7477 443; fax: +358 20 7477 305. 0255-2701/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2010.09.006

gloss due to the formation of liquid menisci between particles. As air starts to penetrate the particle structure and particles are forced together by increasing capillary forces, a second critical concentration, SCC, can be detected. A third point, termed inter critical concentration (ICC), has also been proposed [4]. Each of the phases are characterised by different particle/liquid interaction mechanisms and redistribution processes. In industry, however, the FCC is often assumed to be the immobilisation point of the coating [5]. Filter cake formation takes place at the coating/base substrate interface due to absorption of the continuous (liquid) phase into the base substrate. Solid material not absorbed will accumulate at the interface, giving rise to an increased solids concentration as compared to the bulk coating suspension. Furthermore, at the surface of the coating, a separate high solids concentration region, termed skin, can be formed due to evaporation of liquid phase from the top of the coating. Although the specific formation mechanism has been a subject of discussion in the literature, there are several empirical and theoretical investigations supporting their existence [6–9]. For instance, Cardinal et al. [10,11] utilised mathematical expressions as well as advanced experimental methods based on the Cryo-SEM technique. They proposed “Drying Regime Maps” for estimating the often complex combination of conditions under which filter cake formation and skinning can be expected to occur. The colloidal interactions between particles in a pigment coating suspension have been observed to impact the structure formation of the coating layer during consolidation [12–14]. Micro-scale par-

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ticle interactions influence observable macroscopic properties in both wet coating suspensions (e.g. viscosity) and in consolidated coatings (e.g. porosity). Adjustments to the colloidal interactions, typically by addition of process chemicals to the coating formulation, can be a cause of both runnability problems and quality defects in the final end product. Although the incentive for understanding the influence of colloidal suspension properties has mostly sprung from troubleshooting, it might also be possible to adjust the properties of the coating formulation to obtain a coating layer of desirable structural properties. As shown by Sand et al. [15], the microstructure development of the coating layer can vary significantly even within typical colloidal parameter intervals [16]. In pigment coating research, modelling and simulation has become evermore established as a complement to empirical methods. The increasing computational resources in combination with improved reliability and sophistication of the models used are enabling unprecedented prediction and explanation of coating system behaviour [17,18]. Simulations have been performed both with simple deposition models [19–21] and deterministic particle dynamics models, which have included hydrodynamics, colloidal interactions and other force models [22–24]. This paper utilises a modified Stokesian dynamics technique to simulate pigment coating layers. In order to identify particle clustering mechanisms and microstructures that control coating layer consolidation. In specific, the influence of drying strategy and colloidal suspension properties are investigated. By understanding the influence of different process conditions and coating suspension properties, the work aids in the tuning of process parameters and coating formulations in order to obtain a coating layer with the desired properties. This paper furthers the work presented in previous publications [2,15,25–27], which focused on immobilisation times, dry solids profiles and particle distributions within the coating layer. 2. Methods The Stokesian dynamics simulation approach was 1987 presented by Barnes et al. [28] as a method for simulating the behaviour of particles suspended in liquid. The first computational code was developed by Brady and Bossis in 1988 [29], partly based on convergence expressions provided by Koliha [30] and O’Brien [31]. In 1990, the Stokesian dynamics technique was for the first time applied to paper coating applications [32]. The simulation method used in this work is based on a modified version of Stokesian dynamics, developed by Toivakka [22] and Nopola [33]. In addition to hydrodynamic interactions, it includes DLVO-type (Derjaguin, Landau, Verwey, Overbeek) colloidal interactions, a free surface model and the Brownian motion. The Stokesian dynamics technique is based on the coupled Nbody Langevin equation [29] m

dU(t) = FH + FP + FB dt


The equation is a variant of Newton’s second law of motion and simply states that mass, m, times acceleration, which is given by the translational and rotational velocity vector U(t), is the arithmetic sum of all forces and torques exerted on a particle. These can include hydrodynamic forces and torques, FH , external or internal deterministic non-hydrodynamic forces and torques, FP , and stochastic forces and torques giving rise to the Brownian motion, FB . The particle Reynolds number [22,33] can be defined as Rep =

l achar uchar , 


where l is the density of the liquid phase, achar the characteristic particle size, uchar the characteristic velocity of the particles rela-


tive to the surrounding liquid and  the viscosity of the suspension. Given a small particle Reynolds number (Rep  1), a simplification can be made to Eq. (1). For low flow rates or for small particles, the inertia of particles can be considered insignificant as the time needed for the particle momentum to relax is much shorter than the time scale for any significant movement of particles [34]. Therefore, if the particle Reynolds number is small, the left hand side of Eq. (1) can be set equal to zero (assuming Rep = 0). For pigment coatings, the liquid medium is most often water and the suspended particles are in the nm to ␮m size range. As the velocity of particles relative to the liquid typically does not exceed a few tens of ␮m/s, the small particle Reynolds number condition applies. Consequently, the hydrodynamic forces will balance the external forces and the total net force on a particle becomes zero. As the particle Reynolds number approaches zero, Eq. (1) can be rewritten RU = −FP − FB ,


where the hydrodynamic force and torque vector, FH , is determined by the resistance matrix R and the velocity vector U [22]. The forces that are determined by both particle velocities and positions are defined in R. The external particle forces independent of particle velocities are defined in FP and the Brownian motion is defined in FB . Long range interactions are included as drag forces and torques according to Stokes law along the diagonal of the resistance matrix R. The Stokes drag contribution is used to take into account the influence of the liquid flow, when calculating the movement of particles. As the motion of particles does not influence the flow of the liquid, phenomena such as hindered settling [35] are not taken into account. This can be a cause of inaccuracy not only in sedimentation-type simulations, but also to some extent when simulating drying. However, in consolidation simulations where the dominating mechanism of dewatering is liquid absorption into a base substrate, the induced error is expected to be small. As a result of this simple division of forces and torques it becomes relatively straight-forward to include additional interaction models, capturing new aspects of the physics of the systems under investigation. The hydrodynamic interaction models have been extensively reported by Sand et al. [36] and are therefore omitted from this paper. As this work is focused on the influence of colloidal interactions, these models are here discussed somewhat more in-depth. The colloidal interaction model can be expressed by a combination of electrostatic repulsion and van der Waals attraction forces. The P , is of DLVO type, given by resulting net colloidal force, Fcoll P P P = Fel + Fvdw . Fcoll


The attractive and repulsive components are given in (5) and (7). The electrostatic repulsion component is expressed as a pairwise short-range repulsive force [37,38], P Fel = 4εr ε0


a1 a2 e− , a1 + a2 1 + e−



where  is the reciprocal electrostatic double layer thickness, εr is the dielectric constant of the continuous phase, ε0 the permittivity of vacuum, 1 and 2 the surface potentials of the interacting particles and  the surface separation distance. a1 and a2 are the radii of the particles. The reciprocal double layer thickness can, for a symmetric and asymmetric electrolyte, respectively, be approximated as


√ 3.29 × 109 |z| c

2.32 × 109 |z|

zi2 ci


where z is the valence and c the concentration of the ions [39].



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The van der Waals attraction component can be estimated using an expression derived from [22,33,37,38] as P = −AH Fvdw

a1 a2 ( + 22.232) , a1 + a2 62 ( + 11.116)2


where AH is the Hamaker constant,  the London characteristic wavelength [40]. In addition to the electrostatic repulsion and van der Waals attraction model, a Born repulsion-type model was utilised for particles in close contact. Born repulsion results from overlapping of electron clouds of two or more particles, and gives rise to a very strong repulsive force [39]. In this work, the Born repulsion model gives a strong repulsive response for particles closer to each other than a defined particle surface roughness (0.1 nm). This prevents particles from overlapping each other. A free surface model was included to account for particles approaching and penetrating the liquid surface. The interaction between a particle and the liquid surface was modelled using a hydrodynamic force for submerged particles, which was transformed into a surface tension-type spring force for particles penetrating the surface. This approach is described in detail by Sand [41] and Toivakka et al. [42]. The approach can be considered as a simplification of the relatively complex particle-free surface interactions as analysed by Geller et al. [43]. Similarly, the Brownian motion model is described in Sand [41]. As the model is developed for concentrated colloidal particle suspensions, it is valid only from the point of coating suspension application up to SCC, i.e. when air starts to penetrate the particle structure. This does not, however, severely limit the applicability of the method, since the greatest particle movement and redistribution is expected within this interval. Liquid bridging and van der Waals forces can be expected to dominate at later stages. This promotes the rigidity of the structure at the later stages of the consolidation. The microstructure development with particle dynamics calculations is analysed with in-house developed particle system visualisation tools. A simple method was developed for identifying and studying cluster formation in particle systems. A threshold value is selected for interparticle surface separation, below which particles are considered to be clustered. Separate regions of high particle concentration are identified as separate clusters, which are distinguishable by a colour code. It is also possible to visualise connections between clustered particles, where the connection can be coloured depending on the surface distance between a particle pair. Using interparticle separation threshold values it is possible to extract clustered regions with locally increased solids concentration, such as in the skin or the filter cake. The threshold values can be arbitrarily selected and can thus give the possibility to highlight interesting structural properties of a particle system. Visualisations using this type of filtering methods can therefore be very useful. Nevertheless, image analysis using manual thresholding approaches has also been subject of criticism, and some caution should be exercised [39,44]. For a more diverse view of the particle system structures described in this work, we also refer to other publications by Sand et al. [2,15,25–27,45,46].

Reynolds and Peclet number. Similarly, a dimensionless expression can be formulated to assess the relative importance of the viscous (hydrodynamic) forces and the colloidal interaction forces. Though these numbers indicate the relative influences of the three dominating force models, hydrodynamic, Brownian and colloidal forces, their values should only be considered as indicative. As a simulation is composed of a fairly limited number of interacting particles in a complex system with constantly changing conditions, many of the variables of the equations above will be particle pair specific and may also change with time. Considering that the particle system is generated with a size distribution, all other parameters being the same, the ratios will still be different for different particle size fractions. 3.1. Hydrodynamics The impact of the hydrodynamic forces of the suspending liquid on the particles can be described using the particle Reynolds number, Rep . The particle Reynolds number can be calculated using the equation Rep =

l achar uchar , 


where l is the density of the continuous (liquid) phase, achar the characteristic particle size, uchar the characteristic velocity of the particles relative to the liquid and  the viscosity of the liquid phase [47]. In the simulation technique used in this work, the particle Reynolds number plays an important role due to the lubrication approximation, which assumes particles to react instantaneously to the flow of liquid. This assumption is only valid, however, for small particle Reynolds numbers. In pigment coating processes, it is possible to estimate the particle Reynolds number given the size scale of the suspended particles, the properties of the suspending liquid and the flow field. During typical paper coating consolidation processes, the particles are within the nm to ␮m size range. The suspending liquid phase is water and the flow rate of the liquid relative to the particles does not exceed a few tens of ␮m/s. Under these conditions, the particle Reynolds number will be in the order of 10−7 –10−11 . Thus, viscous forces will completely dominate over inertial forces and the low particle Reynolds number condition applies. The above analysis applies for consolidation of coating colour after the metering process. Under and in the vicinity of the coating blade, the situation might be different due to high velocities and diverging streamlines in the flow. 3.2. Brownian forces The Peclet number, Pe, is used to compare the convective effect with the effect of particle diffusion. It can thus be utilised to in estimating the relative influence of hydrodynamic forces to diffusion. Convection in this work is driven by liquid absorption into the substrate and evaporation from the free surface, while diffusion results from the Brownian motion. For the current problem, the Peclet number can be expressed as 6achar Huchar , kT

3. Theoretical considerations

Pe =

The interactions and forces discussed above can be evaluated in order to determine which models are relevant to include in simulations. This is done by calculating the forces based on variables and parameter values typical for coating processes. By forming ratios between these forces, it is possible to identify the forces that dominate under specific process conditions. The mutual relevance of hydrodynamics, thermal motion and colloidal interactions are commonly described by the particle

where  is the viscosity of the liquid phase, H is the characteristic length scale of the system (coating layer thickness), k is the Boltzmann constant and T is temperature. uchar is the velocity of the particles relative to the liquid, but can in the case of evaporation also be the velocity of the receding free surface. The Peclet number can therefore be used both in predicting filter cake formation and skinning [10,11]. Peclet numbers larger than one indicate that the effect of diffusion is negligible [39].


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The calculation of the Peclet number is not straight-forward in pigment coating consolidation simulations, since many of the conditions change during the consolidation process. However, when considering values relevant to the simulations of the present work, it can be concluded that the Peclet number can vary significantly during the course of a simulation. For instance, its value can be close to 10,000 at the early stages of consolidation, and for large particles experiencing rapid dewatering/evaporation. On the other hand, it can be below one for the smallest particles during minimal dewatering/evaporation. The calculated ratios results from the parameters; achar = 2 ␮m, H = 5 ␮m, uchar = 30 ␮m/s, T = 298 K and achar = 0.2 ␮m, H = 1 ␮m, uchar = 1 ␮m/s, T = 353 K, respectively. The characteristic length scale above need to be chosen such, that movement of particles over this length scale would have a significant effect on the microstructure of the coating layer and its properties. The consideration above indicates that the effect of Brownian motion in simulations is mostly insignificant. However, it could possibly have an effect for the smallest particle size fraction at the late stages of consolidation. As previously discussed, pigment coating formulations can also include polymeric additives and soluble binders, for which the Peclet number would be even smaller. It should also be noted that the Brownian motion may have an effect on the structure formation by helping particles to rearrange and move past one another.


Fig. 1. Consolidation of a coating layer at the LLH drying strategy ( = 50 mV, 1/ = 5 nm). Particles are coloured according to their local velocity. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

3.3. Colloidal interactions The relative impact of hydrodynamics in relation to colloidal interactions can be formulated by an expression similar to the Peclet number. The expression, here termed Kcoll , can be written Kcoll =

achar uchar P + FP Fel vdw



where values below 1 indicate a higher relative influence of colloidal forces. Estimating from the parameters of the simulations in this work, as also partly discussed above, it can be concluded that this ratio can vary from 0.15 towards infinity. Typically, the relative influence of colloidal forces can be expected to dominate at the latter stages of consolidation while the hydrodynamics dominate at the beginning.

4. Simulation setup Particle systems of fine-grade ground calcium carbonate (GCC) corresponding size distribution and 65 wt.% dry solids content were simulated [15]. The distribution is comparable to the commercial product CoverCarb CC75 (Omya Ag, Switzerland) determined by sedimentation using a Malvern Instruments Zetasizer 3000. The

distribution roughly satisfies the log-normal distribution described by the equation

p(d) =

1 −(d − d ) √ exp 2 d2 d 2




where the mean particle diameter, d , is 1.5 ␮m and the standard deviation, d , 10.0 ␮m. A size fraction cut-off was applied for particles smaller than 0.2 ␮m and larger than 2 ␮m in diameter. This was necessary to limit the number of particles in the system. More details on the size distribution used and the particle system generation can be found in Sand et al. [15]. The initial post-metering thickness of coating layers was set to 30 ␮m, which was shown in earlier studies [2] to be sufficiently thick for identifying coating layer microstructures. An illustration of a simulated consolidation is shown in Fig. 1. Dewatering from the coating layer was simulated by a combination of top side evaporation and absorption by the base substrate as estimated by macroscopic modelling (Coatman, VTT Energy, Jyväskylä) of pilot trial measurements [48]. In the macroscopic modelling, the drying of the coating was conducted in three steps. Each step could be either high or low in intensity, which enabled various dryer setups to be tested. Thus, the high intensity step could be used to simulate infrared drying, while the low intensity step would correspond to air foil or cylinder drying. More information

Fig. 2. Drying strategies generated from macroscopic modelling and based on pilot trials [48].


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Table 1 Colloidal interaction model parameters. Symbol


Electrostatic repulsion parameters εr 80

ε0 1,


8.85 × 10−12 (C2 /Nm2 ) −50 to +50 (mV)

1/ 2.5–10.0 (nm) Van der Waals attraction parameters 1 × 10−21 (J) AH  100 × 10−9 (m)

Description Continuous phase dielectric constant (water) Permittivity of vacuum Surface potential of interacting particles Double layer thickness Hamaker constant London characteristic wavelength

is given in Timofeev et al. [48]. In this work, two different drying strategies were studied; a Low-Low-High case, implying 2 mild drying steps at the start followed by more intense drying, and a High-Low-Low case, with initially intense drying followed by mild drying at the end. The simulation domain was restricted by a planar boundary at the bottom, which allows permeation of liquid. Particles are therefore deposited at the surface of the base substrate. Evaporation is simply defined as the expelling of liquid at the top of the coating, i.e. at the suspension/air interface. The drying strategies are described in detail by Sand et al. [2]. The relationship between absorption and evaporation, and their time dependency, is shown in Fig. 2. As concluded in previous work [15], the colloidal properties of the suspension strongly influence the consolidation of the coating layer. In this work the same parameter selections were used, as based on experimental measurements and literature sources [16,49,50]. The parameters were selected to as closely as possible resemble what can be expected in an industrial paper coating process. For instance, partners in the KCLCONS project, Eriksson et al. [16], performed measurements on the same pigment system as simulated in this work. The parameter selection in this study was partly made based on those results. The colloidal parameters are shown in Table 1, while details on the models and more in-depth description of the parameter selection can be found elsewhere [15,45,46].

Fig. 3. Structure analysis of the HLL coating layer at 0.2 s using the 50 and 0 mV particle surface potential cases. Clusters are coloured according to their relative size (red = largest, blue = smallest), while non-clustered particles are grey. (A) subfigures represent particle cluster visualisations, while (B) subfigures show interparticle connections between clustered particles (also including adjacent cells). The surface separation threshold value used is 50 nm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

5. Results and discussion In this work, particle clustering algorithms along with particle system visualisation were utilised in studying the structure formation of consolidating coating layers. This is in contrast to similar studies [2,15,45], which utilised z-direction solids curves in describing the microstructure of coating layers. The results reported cover the time ranging from coating suspension metering and roughly until the SCC where air starts to penetrate the system.

Fig. 4. Consolidation of the LLH layer at particle surface potential 50 mV (left) and 0 mV (right) (1/ = 5 nm, clustering threshold 50 nm, dark particles are clustered).

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Fig. 5. Consolidation of the HLL layer at two different double layer thicknesses, 2.5 nm and 10 nm (

In some cases, for illustrative purposes, this time is extended by a few tens of seconds beyond SCC. For estimated immobilisation times we refer to Sand et al. [2,25], which reports values in the range of 0.3–0.5 s after metering. As found by Sand et al. [15], the particle surface potential had very small systematic influence on the internal microstructure development. There was a clear correlation, however, with the thickness of the coating layer. The visualisation of consolidation using the HLL drying strategy in Fig. 3 compares the 0 and 50 mV cases of particle surface charge at a constant electrostatic double layer thickness, 10 nm. Fig. 3 illustrates particle clustering both through colour codes (A) and by “network connections” (B). Network connections are produced by plotting contact lines between particles belonging to a cluster. It can be seen that at a high particle surface potential, which increases interparticle repulsion, particles are able to move past each other to generate denser structure. As a result, mainly the filter cake and skin region are sufficiently dense to generate particle clustering. At the low surface potential, particles are immediately attracted to each other, which generated a loose clustered structure, impeding the shrinkage of the coating layer. As particle wrapping is turned off in the visualisation, we can see that there is significant sideways movement of particles resulting from the rigidity of the structure in combination with the contraction forces on the layer caused by the dewatering. Turning off particle wrapping can be useful for visualisation of lateral movement of particles. This movement is usually masked by the periodic boundary conditions, which require particles that move out of the simulation domain to re-appear at the opposite side. The phenomenon of lateral particle displacement was already observed in previous work [26,27], but the underlying mechanisms could not be sufficiently explained due to the lack of visualisation methods. A similar illustration of the layer consolidating using the LLH drying strategy shows equivalent results, Fig. 4. The 0 mV parti-


= 25 mV, clustering threshold 20 nm, dark particles are clustered).

Fig. 6. Consolidation visualisation using the LLH drying strategy and with 10 nm double layer thickness ( = 25 mV, clustering threshold 20 nm, dark particles are clustered).


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cle surface potential case produced immediate agglomeration of the particle system. The rigidity of the structure, also indicated by extensive lateral direction movement of particles (illustrated by the unwrapped system, as discussed earlier), resulted in significantly reduced shrinkage of the layer. The higher particle surface potential allowed particle rearrangement and gradual consolidation of the layer starting from the filtercake side and continuing until immobilisation into a significantly denser structure as compared to the low particle surface potential case. Adjustments to the electrostatic double layer thickness, which can be influenced, e.g., by electrolyte addition to the coating formulation, had minimal influence on the thickness of the coating layer. For instance, Fig. 5 shows more or less identical final coating layer thicknesses. However, the internal microstructures differ significantly depending on the double layer thickness. As can be concluded from the DLVO interaction curve, particles will “feel” each other at much larger distance if the suspension properties give rise to a thick double layer [15]. Consequently, any solids concentration gradients arising from the drying strategy can readily be counteracted by the electrostatic repulsion of DLVO-related interactions. At a small double layer thickness, however, the LLH dewatering strategy gives rise to notably increased local particle concentration at the coating/base substrate and coating/air interface. As already pointed out in Sand et al. [2], the coating layers subjected to the LLH drying strategy consolidated significantly slower as compared to the HLL strategy, as shown in Figs. 6 and 7. Using

Fig. 8. Cluster connections coloured according to interparticle distance (red = short distance, blue = long distance). HLL drying strategy, = +25 mV, 1/ = 2.5 nm, clustering threshold 20 nm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 7. Consolidation visualisation using the LLH drying strategy and with 2.5 nm double layer thickness ( = 25 mV, clustering threshold 20 nm, dark particles are clustered).

cluster visualisation, it can be seen that the layer immobilises within 0.6–0.7 s. Furthermore, as indicated by the cluster region at 0.5 s, the SCC is probably reached already before the layer is consolidated to its final structure. This is in contrast to the HLL strategy, where there is distinct skinning as part of the layer consolidation, and the layer is fairly immobilised already around the FCC. In the LLH case, evaporation is mild at the beginning of consolidation, which results in the absorption into the base substrate to dominate the internal structure formation of the coating, Fig. 7. In accordance with the conclusions of the HLL drying case, however, this only takes place for the suspension with favourable double layer thicknesses. Thus, through tailoring of the chemical properties of the suspension, it can be possible to at least partly offset the influence of drying strategy on the microstructure formation of the coating. The dewatering rate and therefore also the immobilisation time, will still be influenced by the evaporation rate during drying. By only drawing interparticle connections between clustered particles, it was observed that it is relatively common for “fingered” structures to form. Such structures have previously been reported in 2D simulations of coating layer levelling during drying and in rheological studies [51,52]. A fingered structure is a chain of particles

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in close contact. This may influence the properties of the suspension, such as its rheology. In this case, fingering appears to provide skeletal support for the bulk microstructure during consolidation. This can affect the shrinkage of the coating layer and limit lateral, levelling movement of the particles. An example is shown in Fig. 8, where the fingering effect can be seen arising at 0.2 s and disappear as the layer consolidates further. Finger formations could span over 5–6 particles and represent up to one-third of the coating layer in thickness. Such structures seemed more likely to grow from the filtercake side due to the high relative volume of liquid being dewatered into the base substrate through absorption. At very intense drying conditions, similar effects from the skin side can also be considered possible.

6. Concluding remarks The drying strategy strongly impacts the consolidation and microstructure of pigment coating layers. The extent of filter cake formation at the coating/base substrate interface and skinning at the coating/air interface typically depend strongly on the drying strategy applied. Colloidal interaction parameters had a profound influence on both the internal microstructure formation of the coating layer and on the coating thickness development. The effects of alterations to particle surface potential and electrostatic double layer thickness were easily distinguishable from each other. It should be noted, however, that these parameters to some extent are interrelated and difficult to adjust separately in experimental studies on coating processes. The particle surface potential had very small systematic influence on the solids concentration profile within the coating layer, while having a strong impact on the thickness of the coating layer. Cluster visualisation showed that the domination of particle attractive forces at low particle surface potentials generated relatively rigid and porous particle clusters, which supported the higher coating layer thickness. The effect of strong particle clustering at low particle surface potentials was observed regardless of drying strategy. The electrostatic double layer thickness did not influence the thickness of the coating layer to any significant extent. The potential for forming inter-structural solids concentration gradients, however, depended on the thickness of the double layer. The dewatering of the coating layer determined the locations of the regions with higher and lower particle concentration. At low double layer thickness, the initially intense drying strategy (HLL) generated low porosity regions at both the filter cake side and at the top of the coating layer. The initially mild drying (LLH) produced high particle concentration at the filter cake, while no skinning was observed at the top of the coating. At high double layer thickness, the repulsion between particles was strong. In this case, the internal structure formation of the coating did not depend to any significant extent on the drying strategy. It was also found that fingering effects quite commonly arise in consolidating layers. Such formations might also have influence on the consolidation and microstructure of pigment coating layers. It should be noted that smaller application amounts, 15 ␮m in coating layer thickness or less, lead to faster consolidation the layer and does not necessarily give rise to similar concentration gradients as observed in this work [2]. Cluster visualisation was found to be a useful tool in highlighting and explaining concentration differences and particle agglomeration in particle systems. Clustering mechanisms influencing the macroscopic properties of the coating could also be identified. The work illustrates the interplay between the properties of the pigment suspension and the drying strategy in forming the structure of


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